Interferometer system, method for recording an interferogram and method for providing and manufacturing an object having a target surface

ABSTRACT

An interferometer system comprises a reference surface, a support for an object providing an object surface, a radiation source for emitting radiation of an adjustable frequency onto the reference surface and the object surface, a position-sensitive radiation detector, a controller for adjusting a plurality of different frequencies of the radiation emitted by the radiation source, and an integrator for averaging the interference patterns superposed on the radiation detector at different frequencies. Moreover, there is provided a method for recording an interferogram, a method for providing an object with a target surface as well as a method for manufacturing an object with a target surface.

[0001] This application is a continuation of International ApplicationNo. PCT/EP02/07080 filed on Jun. 26, 2002, which InternationalApplication was published by the International Bureau on Jan. 9, 2003,and which was not published in English, the entire contents of which areincorporated herein by reference. This application also claims thebenefit of DE 101 30 902.3 filed on June 27, 2001, the entire contentsof which are incorporated herein by reference.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The present invention relates to an interferometer system and amethod for recording an interferogram. The interferometer system and themethod are preferably used to determine topological properties of anobject surface from the interferogram by evaluating the recordedinterferogram.

[0004] Furthermore, the invention relates to a method for providing andmanufacturing an object having a target surface, wherein deviationsbetween the target surface and an actual surface of the object aredetermined from an interferogram and wherein the object is provided orreworked dependent upon such deviations.

[0005] 2. Brief Description of Related Art

[0006] Usually, interferometer systems are used, among others, todetermine topological properties of an object surface. To this end, forexample, a known reference surface and an object surface to be measuredare illuminated with coherent radiation, and an object wave fieldreflected from the object surface and a reference wave field reflectedfrom the reference surface are superimposed on e.g. a screen such thatan interference pattern is generated thereon. From the interferencepattern a difference between the optical paths from the referencesurface to the screen and from the object surface to the screen may bedetermined position-dependently. From such differences topologicaldifferences between the object surface and the reference surface maythen be determined.

[0007] Two techniques are commonly applied to determine such pathdifferences with an interferometer system:

[0008] A first approach is the so-called fringe pattern interferometery“FPI”, wherein an optical path difference between two wavefronts isdetermined from positions of fringe centers of an interference pattern.In this respect, reference can be made, for example, to R. A. Jones andP. L. Kadakia, “An Automated Interferogram Technique”, Applied Optics,vol. 7, pp. 1477-1482 (1968); Zanoni, U.S. Pat. No. 4,159,522, publishedJun. 26, 1979 and Zanoni, U.S. Pat. No. 4,169,980, published Oct. 2,1979.

[0009] Another approach is the so-called phase measuring interferometry“PMI”, wherein the phase difference between the two wavefronts iscalculated for each pixel of a detector from a plurality of interferencepatterns, said plurality of interference patterns being recorded in thatdifferent phase differences are generated therein. In this respect,reference can be made, for example, to J. H. Brunning et al., “DigitalWavefront Measuring Interferometer for Testing Optical Surfaces andLenses”, Applied Optics, vol. 13, pp. 2693-2703 (1974); Gallagher etal., U.S. Pat. No. 3,694,088, published Sep. 26, 1972, N.Balasubramanian, U.S. Pat. No. 4,225,240, published Sep. 30, 1980; M.Schaham, Proceedings SPIE, vol. 306, pp. 183-191 (1981); and H. Z. Hu,“Polarization heterodyne interferometry using a simple rotatinganalyzer. 1: Theory and error analysis”, Applied Optics, vol. 22, pp.2052-2056 (1983).

[0010] From U.S. Pat. No. 4,594,003 there is known an interferometersystem in which the frequency of the radiation source is variable sothat the fringes of the interference pattern can be displaced without anoptical component of the interferometer system, such as a referencesurface or an object surface, having to be mechanically shifted. In saidsystem, it is provided for a change over such a range that the fringesof the interference pattern are displaceable over a full fringe width.Four interference patterns are recorded, namely with four differentfrequencies of the radiation source distributed within said range. Foreach pixel of the detector a phase φ of the optical path difference isthen calculated according to the following formula:${{\phi \left( {x,y} \right)} = {\arctan \left( \frac{{B(0)} - {B(2)}}{{B(1)} - {B(3)}} \right)}},$

[0011] wherein B(0) to B(3) are the intensities of the individual imagesat the respective pixel.

[0012] This known method for determining path differences is lesssuitable if there is a further surface present in the interferometersystem which likewise reflects a wave field which interferes with thewave fields reflected by the reference surface and the object surface.The resulting interference pattern is then of a particular complexnature. This situation occurs, for example, if a surface of atransparent plate with two substantially plane-parallel surfaces is tobe measured.

SUMMARY OF THE INVENTION

[0013] It is an object of the present invention to provide aninterferometer system and a method for recording an interferogram whichis less sensitive to disturbing reflections.

[0014] Moreover, it is an object of the invention to provide a methodfor providing and manufacturing an object with a target surface.

[0015] In this respect, the invention proceeds from an interferometersystem comprising a reference surface, an object surface, a radiationsource for illuminating the reference surface and the object surfacewith radiation of an adjustable frequency and a position-sensitiveradiation detector. The radiation source, the reference surface, theobject surface and the detector are disposed such that a reference wavefield reflected from the reference surface is superimposed with anobject wave field reflected from the object surface to form aninterference pattern with a position-dependent intensity distribution,said interference pattern being imaged onto the detector. Here, theinterference pattern formed by superposition of the reference wave fieldand the object wave field is disturbed by a disturbing wave field whichis likewise superimposed on said wave fields, said disturbing wave fieldbeing reflected from a disturbing interference surface which isilluminated by the radiation source together with the reference surfaceand the object surface, respectively.

[0016] The invention is distinguished in this respect by an integratorfor position-dependent averaging of a plurality of interference patternswhich are recorded at different frequencies of the radiation emitted bythe radiation source.

[0017] The resulting interferogram is thus generated such that for eachposition of the interferogram an average is formed from the intensitiesof the individual interference patterns at said position. Herein, theaveraging is preferably a weighted averaging.

[0018] The weighting factors for the weighted averaging or/and thevalues of the different radiation frequencies are preferably set as afunction of the distance of the disturbing interference surface from theobject surface and the reference surface, respectively. Preferably,these values are set such that an influence of the disturbing wavefronton the interferogram is substantially averaged out. The interferogramformed by averaging a plurality of interference patterns is then of sucha configuration and intensity distribution, respectively, whichcorresponds approximately to that which would be generated by thewavefronts reflected from the object surface and the reference surfacealone as if the disturbing interference surface were not present in theinterferometer system.

[0019] In this respect, it is further advantageous for the optical pathdifference between the reference surface and the object surface to beadjustable, since by appropriately selecting these distances relative toeach other, an influence of the disturbing wavefront on theinterferogram can be further reduced.

[0020] It is advantageous for the plurality of frequencies for producingthe plurality of interference patterns to be adjusted successively intime over a period of time which corresponds to an exposure timeinterval of a camera which records the interference patterns. Thisenables a particular simple design of the integrator since it is thenformed by the camera itself.

BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Exemplary embodiments of the invention will be illustrated withreference to drawings below, wherein

[0022]FIG. 1 is an embodiment of an interferometer system according tothe invention,

[0023]FIG. 2 is a diagram illustrating differing frequencies ofradiation emitted by a radiation source of FIG. 1 for generatinginterference patterns,

[0024]FIG. 3 shows a time dependency of the radiation emitted from theradiation source of FIG. 1,

[0025]FIG. 4 is a diagram showing an interferogram intensity as afunction of an optical path difference for an interference patterngenerated by the interferometer system of FIG. 1 when the frequenciesare set in accordance with FIGS. 2 and 3,

[0026]FIG. 5 shows an interferogram modulation as a function of anoptical path difference in the interferometer system of FIG. 1 whichresults from another time-dependent setting of the frequencies of theradiation source,

[0027]FIG. 6 shows a frequency distribution corresponding to FIG. 2 ofthe radiation emitted from the radiation source,

[0028]FIG. 7 is a representation corresponding to FIG. 4 of theinterferogram intensity as a function of the optical path lengthdifference when using the frequency distribution shown in FIG. 6,

[0029]FIG. 8 is a partial view of a further embodiment of theinterferometer system according to the invention, and

[0030]FIG. 9 is a partial view of a further embodiment of theinterferometer system according to the invention.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

[0031]FIG. 1 shows a Fizeau interferometer system 1 for measuring asurface 5 of a plane-parallel plate 3. The plate 3 is fixed in a support4 which is displaceable relative to a reference surface 23 by means of amotor drive 6.

[0032] The interferometer system 1 comprises a light source 9 whichemits a beam 11 of coherent light with adjustable wavelength andfrequency, respectively. The light source 9 is a so-called ECDL source,i.e., a diode laser with adjustable external cavity (external cavitydiode laser).

[0033] Such an ECDL radiation source is, for example, described in thearticle “Widely Tunable External Cavity Diode Lasers” by Tim Day,Michael Brownell and I-Fan Wu. Corresponding sources can be obtainedfrom the company New Focus, Inc., 1275 Reamwood Avenue, Sunnyvale,Calif. 94089, USA.

[0034] The beam 11 emitted by the source 9 is focused by a lens 13 ontoa rotating ground glass plate or diffusing plate 15 for suppressingspatial coherence of the radiation. The diffusing plate 15 rotates aboutan axis of rotation not shown in FIG. 1.

[0035] After having passed through the focus in the region of thediffusing plate 15, the expanding beam 11 traverses a semi-transparentmirror 17 and, after having been sufficiently expanded, is then renderedparallel by a collimator 19 which may comprise one or more lenses. Thethus parallelized beam 11″ passes through a glass plate 21 whose surface23 facing away from the collimator 19 forms the reference surface formeasuring the surface 5 of the plane-parallel plate 3. The referencesurface 23 is provided as flat as possible. A surface 25 of the plate 21facing towards the collimator 19 extends at an angle with respect to thereference surface 23 so that radiation reflected from said surface 25 isnot reflected back upon itself and does not contribute to disturbinginterferences.

[0036] Radiation reflected back upon itself from reference surface. 23is again collimated by the collimator 19, impinges on thesemi-transparent mirror 17 and is imaged by the mirror, after havingpassed through an aperture 27 and an ocular 29, onto aradiation-sensitive layer 31 of a CCD camera 33. A part of the beam 11passing through the reference surface 23 impinges on the surface 5 ofthe plane-parallel plate 3 to be measured. The surface 5 to be measuredis oriented as orthogonally as possible in respect of the direction ofthe parallel beam 11″. A portion of the radiation impinging on thesurface 5 to be measured is, again, reflected back upon itself, passesagain through the plate 21 and is likewise focused by the collimator 19and imaged on the radiation-sensitive surface 31. Theradiation-sensitive layer 31 of the camera 33 thus forms a screen onwhich the radiation reflected back from the reference surface 23interferes with the radiation reflected from the surface 5 to bemeasured.

[0037] It is one purpose of the interferometer arrangement 1 to detectthe interference pattern generated by the interfering superposition ofthe radiation reflected back from the reference surface 23 and theradiation reflected back from the surface 5 to be measured.

[0038] As already mentioned above, the plate 3 is, however, aplane-parallel plate, that is, the surface 5 of the plate 3 to bemeasured and a back surface 7 of the plate 3 opposed thereto extendsubstantially parallel to each other. This results in that a portion ofthe radiation 11 passing through the surface 5 to be measured islikewise reflected back upon itself from the back surface 7 of the plate3 and imaged on the radiation-sensitive layer 31.

[0039] Accordingly, on the one hand, the radiation reflected back fromthe reference surface 13 interferes on the radiation-sensitive layer 31with the radiation reflected back from the surface 5 to be measured, anoptical path length difference therebetween being 2·C₀, and, on theother hand, the radiation reflected from the reference surface 23interferes on the radiation-sensitive layer 31 with the radiationreflected from the back surface 7 of the plane-parallel plate 3, anoptical path length difference therebetween being 2·C₂, and,furthermore, the radiation reflected from the surface 5 of the plate 3to be measured interferes there with the radiation reflected from theback surface 7 thereof, an optical path length difference therebetweenbeing 2·C₁. The interference pattern generated on theradiation-sensitive layer 31 is thus very complicated and difficult toevaluate.

[0040] The camera 33 supplies the data which are representative of aradiation intensity distribution on the radiation-sensitive surface 31via a data line 35 to a computer 37.

[0041] The computer 37, in turn, generates a representation of theinterference pattern on the radiation-sensitive layer 31 on a display39, an interference pattern being represented merely schematically inFIG. 1 by a plurality of fringes 40. Further, the computer 37 stores thedata and also performs an evaluation of the interference pattern todetermine therefrom level differences between the reference surface 23and the surface 5, to be measured, and the topology of the surface 5 tobe measured, respectively.

[0042] Moreover, the interferometer system 1 comprises a controller 41which is supplied, via a control line 43, with frequency data and whichis triggered by the computer 37, said controller then setting,time-dependently, via a line 45 the frequency of the radiation 11 to beemitted from the source 9 in response to a trigger signal 48 generatedby the camera 33 which is also supplied to the computer via a line 47.

[0043] A method for operating the interferometer system 1 is describedhereinbelow, the plate 3 being assumed to have a thickness of 74 mm, sothat, taking the refractive index of the glass of the plate 3 intoconsideration, a resulting optical path difference 2·C₁ of 214.39 mm isprovided.

[0044] First, the controller 41 sets, via line 45, the frequency of theradiation source 9 to a first frequency with a value f−Δf and starts,via line 47, the integration of the CCD camera 33 so that theinterference pattern which is generated by the wavefronts reflected fromthe three surfaces 23, 5 and 7, upon illumination with radiation of thefrequency f−Δf, impinges on the radiation-sensitive surface 31 of thecamera 33, and the corresponding radiation intensity is integratedthere. After 3.75 msec, the controller 41 sets the source 9 to a second,higher frequency f so that interference patterns generated at thisfrequency impinge during the integration time of the camera 33 as secondinterference patterns on the radiation-sensitive layer 31, and thecorresponding radiation intensities are integrated there with theintensities of the first interference pattern. After a further 7.5 msec,the controller 41 sets the frequency of the radiation source 9 to astill higher, third frequency with the value f+Δf so that theinterference pattern generated at this third frequency likewise impingesduring the integration time of the camera on the light-collectingsurface 31 thereof, and the intensities of the third interferencepattern are added to the intensities of the first and the secondinterference patterns. The illumination with the third frequency f+Δflasts for 3.75 sec. After that, the controller 41 causes, via line 47,the integration time of the camera 33 to terminate, and the data whichrepresent position-dependently the entire light intensity which hasimpinged during the integration time on the light-collecting surface 31are read-out and supplied to the computer 37 via line 35.

[0045] The above-described integration time of the camera of 15 msec waschosen in the present embodiment to achieve a high-quality image at thegiven laser power.

[0046] Depending on the laser energy available and other boundaryconditions, it is also possible to set different integration times.

[0047] These data are thus representative of the sum of three differentinference patterns, wherein the first interference pattern was recordedwith radiation of the frequency f−Δf, wherein the second interferencepattern was recorded with the frequency f and wherein the thirdinterference pattern was recorded with the frequency f+Δf. When thethree interference patterns are integrated, the interference patternrecorded at the medium frequency f is weighted with double the weightingfactor as compared to the two other frequencies f−Δf, f+Δf.

[0048] This weighted illumination with three different frequencies isagain illustrated in FIGS. 2 and 3. In FIG. 2, the spectral powerdensity is shown in arbitrary units as a function of the wave number kof the radiation of the source 9. It is apparent that the illuminationwith the three different frequencies is effected with the relativeweighting factors 0.5, 1 and 0.5. This spectral power densitydistribution can be represented as a formula as follows: $\begin{matrix}{{F(k)} = {A \cdot {\quad\left\lbrack {{\frac{1}{2}{\delta \left( {k - \left( {k_{0} - {\Delta \quad k}} \right)} \right)}} + {\delta \left( {k - k_{0}} \right)} + {\frac{1}{2}{\delta \left( {k - \left( {k_{0} + {\Delta \quad k}} \right)} \right)}}} \right\rbrack}}} & {{Equation}\quad (1)}\end{matrix}$

[0049] wherein

[0050] δis Dirac's delta function

[0051] k is the wave number 2π/λ,

[0052] k₀ is the basic wave number 2π/λ₀ and

[0053] Δk is the wave number change corresponding to the frequencychange Δf.

[0054] In the present case, λ₀ was chosen to be 632.8 nm. The radiationsource 9 can be set to this wavelength, and this setting is advantageousin so far as, apart from the radiation source, a structure andcomponents which are known from interferometers operated withconventional He-Ne lasers can be used for the interferometer system.

[0055] The interferogram as Fourier transform of the spectral densitymay be written as $\quad\begin{matrix}\begin{matrix}{{{I(x)} = {\int_{0}^{\infty}{{{F(k)} \cdot \cos}\quad k\quad {x \cdot \quad {x}}}}}\quad} \\{= {{{A \cdot \frac{1}{2}}\left\{ {{{\cos \left( {k_{0} - {\Delta \quad k}} \right)} \cdot x} + {{\cos \left( {k_{0} + {\Delta \quad k}} \right)} \cdot x}} \right\}} + {A \cdot {\cos \left( {k_{0}x} \right)}}}} \\{= {{A \cdot \cos}\quad k_{0}{x \cdot \left( {1 + {\cos \quad \Delta \quad {kx}}} \right)}}}\end{matrix} & {{Equation}\quad (2)}\end{matrix}$

[0056] Accordingly, a beat wave number of Δk results for theinterferogram. A graph of the function I(x) is schematically shown inFIG. 4 for an arbitrary point in the interferogram. An envelope of thedepicted curves is also referred to as interference contrast ormodulation. Accordingly, the modulation periodically increases anddecreases as a function of the distance from the reference surface,wherein the modulation goes down to zero at specific distances.

[0057] An advantageous operation of the interferometer system 1 isprovided when the reflecting surfaces 23, 5, 7 are disposed relative toone another such that the optical path difference 2·C₁ caused by thedistance between the surface 5 to be measured and the back surface 7approximately coincides with the first minimum of the modulationminimum, and such the path difference 2·C₂ caused by the distancebetween the reference surface 23 and the back surface 7 of the plate 3approximately coincides with the second minimum of the modulationminimum, and such that the path length difference C₀ produced by thedistance between the reference surface 23 and the surface 5 to bemeasured approximately coincides with the second maximum of themodulation maximum. To this end, first of all the frequency change Δfand wave number change Δk, respectively, are determined as follows:

[0058] First, 1+cos Δk·C₁ is set to 0, which results in Δk·C₁=π. As, inthe present example, the plate thickness C₁ is assumed to be 214.139 mm,this results in Δk=14.67m⁻¹. Then, the distance of the plate 3 from thereference surface 23 is adjusted via the drive 6 such that Δk·C₂=3π isfulfilled. It should be noted in this respect that the last-mentionedcondition need to be observed only with relative little accuracy, sincethe modulation according to FIG. 4 exhibits quadratic minima and theseare thus relatively insensitive to changes in the optical pathdifference. With the above-illustrated setting of Δk and the distance ofthe back surface 7 from the reference surface 23, the optical pathlength difference 2·C₀ is automatically set to such a value that itapproximately coincides: with the second maximum of the modulationmaximum according to FIG. 4.

[0059] Accordingly, the disturbing interferences caused by the backsurface 7 of the plate 3 are thus effectively averaged out by theweighted averaging carried out during the integration time of the camera33, so that the interferogram obtained by the averaging comprises, apartfrom a constant radiation portion, merely a fringe pattern as it wouldbe generated by the interference solely of the wavefront reflected backfrom the reference surface 23 with the wavefront reflected back from thesurface 5 to be measured. This relatively simple and undisturbedinterference pattern is then subjected to a conventional evaluationmethod for fringe patterns in order to determine on the basis thereofthe topology of the surface 5 to be measured. The operation of theinterferometer system 1 is not limited to control the frequency of theradiation source 9 with the timing scheme shown in FIG. 3. In thefollowing, there is discussed as a variant the possibility to change thefrequency of the radiation source 9 with a sinusoidal time dependency.First, be it assumed here for the interferogram intensity I:

I(x)=I ₀·[1+V·cos(k·x−Φ ₀)],  Equation (3)

[0060] wherein

[0061] k is the wave number of the radiation which can be assumed to beapproximately constant in this formula,

[0062] x is the optical wavelength difference,

[0063] Φ₀ is an interferogram phase and

[0064] V is an interference contrast.

[0065] Due to the sinusoidal frequency change, the interferogram phasethen results into

Φ₀−Φ₀(t)=Φ₀ ′+A·sin ωt,  Equation (4)

[0066] wherein

[0067] Φ₀′ is an average phase value,

[0068] ω is the angular velocity of the phase modulation and

[0069] A is a phase modulation amplitude.

[0070] Inserted into equation (3), it thus follows:

I(x,t)=I ₀·[1+V·cos(k·x−Φ ₀ ′−A·sin ωt)].  Equation (5)

[0071] The modulation period for the frequency change of the radiationis then set such that an integer numbered multiplicity thereofcorresponds to the integration time of the camera 33. The time averagedinterferogram is thus calculated to be $\begin{matrix}{{\overset{\_}{I}(x)} = {{\frac{1}{2\pi}{\int_{- \pi}^{\pi}{I_{0} \cdot \left\lbrack {1 + {V \cdot {\cos \left( {{k \cdot x} - \Phi_{0}^{\prime} - {{A \cdot \sin}\quad \omega \quad t}} \right)}}} \right\rbrack \cdot \quad {\left( {\omega \quad t} \right)}}}} = \quad {{I_{0} + \quad {I_{0} \cdot V \cdot {\cos \left( {{k \cdot x} - \Phi_{0}^{\prime}} \right)} \cdot \underset{J_{0}{(A)}}{\underset{}{\frac{1}{2\pi}{\int_{- \pi}^{\pi}{{\cos \left( {{A \cdot \sin}\quad \omega \quad a\quad t} \right)} \cdot \quad {\left( {\omega \quad t} \right)}}}}}} + {{I_{0} \cdot V \cdot {\sin \left( {{k \cdot x} - \Phi_{0}^{\prime}} \right)} \cdot \underset{0}{\underset{}{\frac{1}{2\pi}{\int_{- \pi}^{\pi}{{\sin \left( {{A \cdot \sin}\quad \omega \quad a\quad t} \right)} \cdot \quad {\left( {\omega \quad t} \right)}}}}}}{\overset{\_}{I}(x)}}} = {I_{0} \cdot \left\lbrack {1 + {V \cdot {\cos \left( {{k \cdot x} - \Phi_{0}^{\prime}} \right)} \cdot {J_{0}(A)}}} \right\rbrack}}}} & {{Equation}\quad (6)}\end{matrix}$

[0072] wherein J₀(A) is the Bessel function of Zero order of the phasemodulation amplitude A. This function is shown in FIG. 5.

[0073] Phase modulation amplitudes A may then be determined such thatinterferences between the wavefronts reflected back from the surface 5to be measured and from the back surface 7 of the plate 3 willdisappear. Accordingly, the frequency modulation amplitude of theradiation source 9 must be set such that the phase modulation for theoptical wavelength difference 2·C₁ corresponds to the first Zero pointof the Bessel function of Equation (6). This is the case forA₁=0.76547·π.

[0074] Furthermore, by changing the distance between the referencesurface 23 and the plate 3, it is achieved that the optical wavelengthdifference 2·C₂ corresponds to the second minimum of the Bessel functionof Equation (6), which is the case for A₂=1.7571·π. The ratio of theoptical path differences is thus given by the two first Zero point ofthe Bessel function J₀(A) $\begin{matrix}{\frac{C_{2}}{C_{1}} = {\frac{A_{2}}{A_{1}} = 2.2955}} & {{Equation}\quad (7)}\end{matrix}$

[0075] On the other hand, C₀=C₂-C₁ is valid, and for the optical pathdifference C₀ to be measured, the amplitude results in $\begin{matrix}{A_{0} = {{\frac{C_{0}}{C_{1}} \cdot A_{1}} = {{\frac{C_{2} - C_{1}}{C_{1}} \cdot A_{1}} = {0.9916 \cdot \pi}}}} & {{Equation}\quad (8)}\end{matrix}$

[0076] At this point, the Bessel function J₀(A) has the value

J ₀(A ₀)=−0.297≈−0.3  Equation (9).

[0077] In this arrangement, three partial beams having an approximatelyidentical basic intensity interfere with each other. However, only thefringe patterns of two interfering partial beams are visible in theweighted averaged, respectively integrated interferogram. The otherinterferences are averaged out, form a constant radiation portion whichreduces the contrast, however. The effective contrast is calculated tobe $\begin{matrix}{V_{eff} = {{V \cdot {J_{0}\left( A_{0} \right)}} = {{\frac{2}{3} \cdot {{- 0.3}}} = 0.2}}} & {{Equation}\quad (10)}\end{matrix}$

[0078] This contrast is sufficient to determine the positions of thefringes 40 and to be able to derive the topology of the surface 5 to bemeasured from the evaluation of the fringe pattern. However, it shouldbe noted that the radiation frequency setting according to the schemeshown in FIG. 3 results in a higher effective contrast.

[0079] In the following, there is described as further exemplaryembodiment for a situation such that the radiation source 9 iscontrolled to emit a Gaussian spectral power density as shown in FIG. 6$\begin{matrix}{{{A(k)} = {\sqrt{\frac{\pi}{2}} \cdot \sigma \cdot ^{- \frac{{({k - K_{0}})}^{2} \cdot \sigma^{2}}{2}}}},} & {{Equation}\quad (11)}\end{matrix}$

[0080] wherein

[0081] k is the wave number 2π/λ

[0082] k₀ is the central wave number 2π/λ₀

[0083] σ is the width of the Gaussian function.

[0084] For this spectral distribution a time-dependent control functionfor the radiation frequency is now to be determined. In this respect,the dependency $\begin{matrix}{\frac{{k(t)}}{t} = \frac{1}{A\left\lbrack {k(t)} \right\rbrack}} & {{Equation}\quad (12)}\end{matrix}$

[0085] is to be observed. This equation may be solved numerically by thecomputer 37 in order to finally obtain a time scheme corresponding toFIG. 3 for the controlling of the radiation frequency.

[0086] With the spectral power density according to FIG. 6, a dependencyof the interferogram intensity on the path difference results as it isshown in FIG. 7. It is evident therefrom that, at small distances fromthe reference surface 23, high interference contrasts are achievable,whereas the contrast is strongly reduced at larger distances from thereference surface 23. This reduction in contrast is so strong that, whenthe plate 3 is positioned closely adjacent to the reference surface 23,interferences which are caused by the back surface 7 are largelyaveraged out, and merely interferences caused by the surface 5 to bemeasured contribute to the fringe pattern of the averaged interferogram.

[0087] This corresponds to an interferogram with a radiation having afrequency which is constant in time and to a reduced coherence lengthwhich is shorter than the optical thickness C₁ of the plate 3. Thetime-dependent frequency change of a radiation source having a largecoherence length thus has an effect which corresponds to a reduction ofthe time coherence for specific lengths. With reference to FIG. 4, thismeans that the time-dependent frequency change has caused the coherenceof the radiation to be destroyed in the regions of the minima of themodulation minima.

[0088] Further variants of the embodiments illustrated with reference toFIGS. 1 to 7 will be described hereinbelow. Components which correspondin their structure and function to those of FIGS. 1 to 7 are designatedby the same reference numbers, but, for the purpose of distinction, aresupplemented by an additional letter. For the purpose of illustration,reference is made in each case to the entire foregoing description.

[0089]FIG. 8 shows a partial view of an interferometer system 1 a whichis similar in construction to the interferometer system shown in FIG. 1.However, the interferometer system 1 a serves to measure a concentricmeniscus lens 3 a rather than a plane-parallel plate. An aplanarcollimator 51 having a plurality of lenses 52 to 56 is positioned in thebeam path downstream of a reference plate 21 a having a referencesurface 23 a, said collimator focussing the parallel radiation 11″a in alocation 57 which further is a center of curvatures of the surfaces 5 aand 7 a of the concentric meniscus lens 3 a.

[0090] Otherwise, the interferometer system 1 a corresponds to theinterferometer system shown in FIG. 1 and is operated according to amethod as illustrated with reference to the interferometer system ofFIG. 1. That is, the frequency of the radiation source is controlled ina time-dependent manner such that disturbing interferences are largelyaveraged out in terms of time which disturbing interferences may becaused by a surface of the concentric meniscus lens 3 a which iscurrently not measured, in particular the surface 7 a, or by otheroptically effective components in the beam path.

[0091] The surfaces 5 a and 7 a of the meniscus lens 3 a can also bemeasured by positioning the lens reversely, that is, it is positioned inthe beam path with its convex surface 7 a disposed towards thecollimator 51 and upstream of the focus 57.

[0092]FIG. 9 shows a variant of the interferometer system shown in FIG.8. In contrast to that system, in the interferometer system 1 baccording to FIG. 9 a reference surface 23 a is not provided on aseparate reference plate but on a precisely fabricated surface of thelens 56 b of an aplanar collimator 51, which surface is disposed towardsthe object to be measured. The interferometer system 1 b, too, serves tomeasure a concentric meniscus lens. Apart from the above-describedtime-dependencies of the frequency of the radiation source forgenerating the interferogram, it is also possible to select othertime-dependencies which are found to be favorable. What is decisive inthis respect is that interference effects which are caused by surfaceswhich are not to be measured are at least partially averaged out overtime.

[0093] The interferometer system was described above as a Fizeauinterferometer. However, it is also possible to use alternativeinterferometer types, such as a Michelson interferometer configurationor a Twyman Green interferometer configuration.

[0094] In the above-described exemplary embodiments, the CCD camera wasused as integrator for the weighted averaging of the interferencepatterns generated at different illumination frequencies. However, it isalso possible to use other camera types which have an integration timewhich is adapted to the sequence of the illumination frequenciesadjusted successively in time. Furthermore, it is possible to generateseparate camera images for several radiation frequencies, to supply thesame to the computer and to carry out the integration and weightedaveraging, respectively, pixel-by-pixel in the computer. The term pixelshould be understood within the scope of the present application to meana resolution unit of the digitalized interference image which isdetermined, among others, by the camera system. Here, the averagingeffected in the computer can also be carried out for groups of pixels,that is, with a resolution which is lower than the camera resolution.

[0095] The above-described interferometer system and the method forrecording the interferogram is advantageously used in a method forproviding an object and in a method for manufacturing an object with apredetermined target surface.

[0096] If, for example, the plane-parallel plate described withreference to FIG. 1 is to be manufactured with high precision, it ispositioned in the beam path of the interferometer system, and aninterferogram is recorded according to the above-described method.Deviations of the surface 5 from the flat nominal shape are determinedfrom the interferogram. On the basis of these deviations, a machiningoperation is planned. In particular, positions on the surface 5 aredetermined from these deviations where a machining operation, inparticular, by further removal of material, is to be effected. After thereworking operation has been carried out, another interferogram istaken, if required, and further reworking operations are effected, ifrequired. If the recorded interferogram shows that deviations betweenthe shape of the surface 5 and the plane nominal shape are less than apredefined value, the plate is provided and shipped.

[0097] This providing and manufacturing method can be applied to anyother object which is to have a predetermined surface. The applicationto a concentric meniscus lens has already been described above. However,other applications for any other objects are conceivable as well.

[0098] The present invention has been described by way of exemplaryembodiments to which it is not limited. Variations and modificationswill occur to those skilled in the art without departing from the scopeof the present invention as given by the appended claims and equivalentsthereof.

What is claimed is:
 1. An interferometer system, comprising: a radiationsource for emitting radiation of an adjustable frequency; a referencesurface; a support for an object providing an object surface; aposition-sensitive radiation detector; a disturbing interferencesurface; a controller; and an integrator; wherein the radiation source,the reference surface, the support and the radiation detector arepositioned such that a first portion of the radiation emitted by theradiation source is incident on the reference surface and reflected as areference wave field therefrom, a second portion of the radiationemitted by the radiation source is directed towards the object surfaceto generate an object wave field reflected from the object surface, andthe reference wave field and the object wave field are superposed toform an interference pattern having a position-dependent intensitydistribution on the radiation detector; wherein the disturbinginterference surface is positioned such that radiation emitted from theradiation source is incident thereon and that a disturbing wave fieldreflected from the disturbing interference surface contributes to theposition-dependent intensity distribution on the radiation detector;wherein the controller is configured for setting the adjustablefrequency of the radiation emitted by the radiation source to aplurality of different frequencies; and wherein the integrator isconfigured for position-dependent averaging the interference patternsformed on the radiation detector at different frequencies.
 2. Theinterferometer system according to claim 1, wherein the radiationdetector comprises a CCD camera.
 3. The interferometer system accordingto claim 1, wherein the integrator is formed by the radiation detector.4. The interferometer system according to claim 3, wherein thecontroller is configured to set the adjustable frequencies to at leasttwo different frequencies during a period of time which corresponds toan integration time of the detector.
 5. The interferometer systemaccording to claim 3, wherein the controller is configured to set theadjustable frequencies to all of the plurality of different frequenciesduring a period of time which corresponds to an integration time of thedetector.
 6. A method of recording an interferogram, comprising:illuminating a reference surface and an object surface with coherentradiation having a frequency; superposing a reference wave fieldreflected from the reference surface and an object wave field reflectedfrom the object surface such that an interference pattern with aposition-dependent radiation intensity distribution is formed ona-screen; and changing the frequency of the radiation successively to aplurality of different radiation frequencies, such that a plurality ofinterference patterns is successively formed on the screen in accordancewith the respective different radiation frequencies; wherein theinterferogram is generated by a weighted averaging of intensities of theplurality of interference patterns at respective positions of theinterferogram.
 7. A method of manufacturing an object having an objectsurface of a target shape, the method comprising: illuminating areference surface and the object surface with coherent radiation havinga frequency; superposing a reference wave field reflected from thereference surface and an object wave field reflected from the objectsurface such that an interference pattern with a position-dependentradiation intensity distribution is formed on a screen; changing thefrequency of the radiation successively to a plurality of differentradiation frequencies, such that a plurality of interference patterns issuccessively formed on the screen in accordance with the respectivedifferent radiation frequencies; generating an interferogram by aweighted averaging of intensities of the plurality of interferencepatterns at respective positions of the interferogram; and machining theobject surface in dependence of the generated interferogram.
 8. Themethod according to claim 7, wherein weighting factors for the weightedaveraging are set by adjusting durations of illumination with therespective different radiation frequencies.
 9. The method according toclaim 7, wherein a disturbing interference surface is disposed at adistance from at least one of the object surface and the referencesurface, wherein the disturbing interference surface is illuminated withthe coherent radiation, and wherein values of at least one of thedifferent radiation frequencies and of weighting factors for theweighted averaging are determined in dependence of the distance.
 10. Themethod according to claims 7, wherein a first optical path differenceexists between an optical path from the reference surface to thedetector and an optical path from the object surface to the detector;wherein a second optical path difference exists between an optical pathfrom the reference surface to the detector and an optical path from thedisturbing interference surface to the detector; wherein a differenceexists between the first optical path difference and the second opticalpath difference; wherein the illumination is performed with a lowerfrequency, a medium frequency, and a higher frequency of the coherentradiation, wherein a frequency difference between the higher frequencyand the medium frequency is equal to a frequency difference between themedium frequency and the lower frequency such that the equation Δk·C ₁=πis fulfilled, wherein Δk is a wave number change corresponding to thefrequency distance, and C₁ is the difference between the first opticalpath difference and the second optical path difference; wherein thedistance between the disturbing frequency surface and the detector isadjusted such that the equation Δk·C ₂=3π is fulfilled, wherein C₂ isthe second optical path difference; and wherein the weighted averagingis performed such that a same weighting factor is associated with theinterference patterns corresponding to the lower and higher frequenciesand that a weighting factor associated with the interference patterncorresponding to the medium frequency is twice the weighting factorassociated with the interference pattern corresponding to the lowerfrequency.
 11. The method according to claim 7, further comprisingdetermining differences between the object surface and the targetsurface in dependence of the generated interferogram, wherein themachining is performed in dependence of the determined differences. 12.The method of claim 11, wherein the machining comprises removing surfaceportions from the object at positions which are determined as a functionof the differences between the object surface and the target surface.